For gravitational modes with \(\ell = 2\)  and \(r_+ = 1\) , there is some confusion over whether \(\omega = -2i\)  is a QNM. It first appears in [1]} with a question mark, it then appears in a graph in [2]}. In [3]}, the authors say they find no evidence for it. Finally it appears again in [4]} (this time without the question mark). We can verify that \(-2i\)  is indeed a QNM. In fact this mode is “algebraically special,"meaning it is purely imaginary and can be identified analytically.
It is easy to verify that \(\omega = -2i\)  satisfies \(\alpha _1^{(4)} =\alpha _1 = 0\)  and \(\beta _1^{(4)}= \beta _1 = 0\) , and thus satisfies Eq. (REF ).
